Talk:certain event

RFD discussion: October 2022–January 2023
Sum of parts: an event that is certain to occur (though our entry is couched in the language of mathematics). Equinox ◑ 16:19, 1 October 2022 (UTC)


 * Delete. Not different from the every-day sense in Four hundred men work in this dizzy height, where a fall means certain death. --Lambiam 13:07, 2 October 2022 (UTC)
 * @Lambiam I think it is different from that every-day sense. is a probability-theory-specific term that builds on the probability-theory-specific meaning of  (which we have as etymology 1, noun, sense 7): "A set of some of the possible outcomes...". Specifically, a certain event is the set of all possible outcomes. Given our current definition, "the Sun will rise tomorrow" is not a certain event. You would have to say "tomorrow the Sun will either rise or not rise" to meet the criteria of containing all possible events. - excarnateSojourner (talk | contrib) 18:07, 4 October 2022 (UTC)
 * People may say that it is certain the Sun will rise tomorrow, but there are several ways in which nature might intervene. The Earth might be destroyed by an extraordinary fast moving . Any time some nearby star may go, annihilating the whole solar system. So probability theory aside, it is not a true certainty. The certainty in probability theory is mathematical certainty, like the certainty that 2 + 2 = 4 – it only exists in the mathematical model, and not in any actual setting modelled that way. That a flipped coin will show heads or tails is not a true certainty – it might remain balanced on an edge. Here, in a textbook, we find a definition of certain: “Event E is certain      E = S&thinsp;”. ( is the event space.) If we want to give a definition that is specific for probability theory, it should be of the adjective .  --Lambiam 19:09, 4 October 2022 (UTC)
 * @Lambiam I agree that certain event is talking about mathematical certainty, not the more common meaning of . That is what I was trying to get at with the example of the Sun rising (just without using math explicitly). I also agree that listing a probability-theory-specific definition at certain rather than certain event would be appropriate, since that textbook quote you gave seems to indicate certain can be used in this sense on its own (as an adjective). So I vote to delete. - excarnateSojourner (talk | contrib) 19:56, 4 October 2022 (UTC)


 * Delete as SOP: whether the current senses of certain cover this or a new mathematical sense is needed, it doesn't seem to be limited to just this phrase. - -sche (discuss) 21:29, 5 October 2022 (UTC)


 * I haven't encountered this term in mathematical literature. Looking a bit through the attestations on Google Books though, some use it as it is defined here, to refer to the universe $$\Omega$$, whereas others seem to use certain event as a misnomer for what is much more commonly referred to as an almost certain event, i.e. any event with measure 1 . It can easily be seen that authors who use it in the former sense are much more mathematically literate than authors who use it in the latter sense. The fact that there are two senses is also reflected in the grammatical definiteness: sense 1 is used definitely, "the certain event", whereas sense 2 is used indefinitely, "a certain event", "any certain event". I vote week keep but I would not be opposed if we said that sense 2 should not be kept because it is a misconstrual of scientific vocabulary, similar to how we don't want to have a spurious sense in a taxonomic entry just because a couple of people were misinformed. to perhaps reconsider in light of the new evidence. &mdash; Fytcha〈 T | L | C 〉 14:30, 4 November 2022 (UTC)
 * The misnoming authors may be unaware of the possibility of proper subsets of $$\Omega$$ that have measure $$1$$, but it is a philosophical issue whether non-empty events of measure $$0$$ can be observable, so perhaps they are not so wrong as their mathematically more literate colleagues may think. Such philosophical issues aside, I think their intended meaning is what one would expect: a certain event is an event that is certain – whether one uses these terms in their everyday senses, or with (possibly non-standard) technical senses --Lambiam 15:44, 4 November 2022 (UTC)
 * I think the issue remains that we first need to settle whether certain is a mathematical term on its own that exists outside the combination certain event ( hinted at something): What else can be certain (in this very sense) other than a mathematical event? Absent any mathematical definition of certain, I think we are forced to keep this term. People seem to (IMO falsely) think that it is not a problem at all intermingle terms from the mathematical realm (event) with non-mathematical terms (certain, pending a new sense). While with event we mean an element of the event space which, ontologically, is a set, certain would be taken to mean any of the presently existing senses in the article . However, it does not appear to be coherent to directly apply these senses to mathematical sets; a set cannot be sure, this would be a category mistake. The standard interpretation for these kinds of mathematical + non-mathematical mixes is that the non-mathematical term is assumed to be associated with an implied (rigorous) mathematical definition which can then be applied to the mathematical term (like when somebody calls a set $$A$$ huge, they mean that there's some subjective and context-dependent cardinal $$\kappa$$ s.t. $$|A|>\kappa$$). I don't see this mechanism to be applicable here because of the divergence in explicit definitions of what it means for an event to be certain. Pinging also who participated in the recent discussion at Talk:convergent sequence. &mdash; Fytcha〈 T | L | C 〉 22:03, 5 November 2022 (UTC)
 * Can certain be used with other terms than event? Certainly. An outcome can be certain:, , . So can an occurrence : , , . Furthermore, one can also say that an event “will occur with certainty”, or that an outcome “will certainly occur”. Outside the realm of probability theory, mathematical entities may also be called certain, for example, logical propositions: , , . --Lambiam 23:27, 5 November 2022 (UTC)
 * These uses all seem to be of a different sense though. The sense for which we want to investigate whether it generalizes to other expressions is the sense of being the sample space (which is the precise sense used in my first two citations). &mdash; Fytcha〈 T | L | C 〉 15:41, 6 November 2022 (UTC)
 * When applied to outcome and occurrence, these form the whole sample space. --Lambiam 20:13, 6 November 2022 (UTC)
 * Hmm. I'm going to maintain my vote because both senses still seep SOP to me (in light of the textbook quote Lambiam gave above). However I have noticed that we have, which by my logic should be deleted (unless it passes the rocking chair test or something). - excarnateSojourner (talk | contrib) 22:42, 4 November 2022 (UTC)


 * Keep per Fytcha. Furthermore, I believe that it is the term "certain event" that is being defined, not just "certain"; the question being asked is, what is it for an "event" to be "certain"? Having the same definition in certain, of the form "of event, such that X" is less convenient for lookup. Thus, it seems to be the case of, which is a pattern especially used in mathematics in Wiktionary: algebraic number, algebraic integer, bound variable, cardinal number, complex number, free variable, imaginary number, rational number, real number, transcendental number, open set, closed set, complete graph, and normal distribution. For each of these terms, it is possible to define them in the adjective only: "Of X, such that Y". Free-variable terms are syntactically unbound: a set is open but it is still the notion of "open set". Compare for evidence of unboundness. --Dan Polansky (talk) 10:21, 5 November 2022 (UTC)
 * Keep per Fytcha and Dan Polansky. Indeed it is the term "certain event" that is at issue. The primary context is the formal basis of probability theory and in particular the definition of probability of an . Part of the formalising process requires defining the "certain event"—the whole sample space, regarded as an event—and specifying that it has probability 1. (It can be expanded on by considering that certain events may be "impossible"—i.e. have probability 0.) The formality becomes more important when establishing the theory for infinite sample spaces of the cardinality of the real numbers, and linking probability theory with measure theory.— Pingkudimmi 05:51, 6 November 2022 (UTC)
 * RFD-kept: no consensus for deletion (WT:VPRFD). --Dan Polansky (talk) 10:44, 4 January 2023 (UTC)